How does the history of the Old West differ from many images of it presented in popular culture?

a. What does a heat engine do? b. How are internal combustion engines different from external combustion engines? How are they similar? c. Why do you think modern cars use internal rather than external combustion engines?

Why can we see steadily and read street signs even though we may be walking or running?

In the lottery game called Florida Lotto, players should select 6 numbers out of 53. Various prizes are offered for matching three through six numbers drawn by the lottery. Florida Lotto sales (in millions of dollars) from 1998 hrough 2011 can be approximated by the function $s ( t ) = - 0.1779 t ^ { 3 } - 2.8292 t ^ { 2 } + 42.0240 t + 698.6831$ where t = 0 represents 1998. The model indicated that $737.7 million in Florida Lotto sales occurred in 1999. Find another year after 1999 when the model indicates that$737.7 million in Florida Lotto sales occurred.

Analyze the phase plane of the differential equations for $x, y \geq 0.$ Show the nullclines and equilibrium points, and sketch the direction of the trajectories in each region.

$$\begin{array}{l}{\frac{d x}{d t}=x(2-x-y)} \\ {\frac{d y}{d t}=y(1-x-y)}\end{array}$$

Some plants that grow in shady areas have dark green or even purple leaves. Come up with a hypothesis to explain this observation.

For $x=a t^{2}$ and $y=b x^{2}$ for nonzero constants a and b, determine whether there are any values of t such that $\frac{d^{2} y}{d x^{2}}(x(t))=\frac{\frac{d^{2} y}{d t^{2}}(t)}{\frac{d^{2} x}{d t^{2}}(t)}$.

Eight years from now, Bianca will be $50\%$ older than she is now. How old is Bianca?

A spherical balloon is inflated with helium at the rate of 100 pi ft^3/min. How fast is the balloon’s radius increasing at the instant the radius is 5 ft? How fast is the surface area increasing?

True/False. The enqueue operation adds an element to a queue.

What is the resistivity of a wire of 5-gauge wire (A = 16.8 $\times$ 10$^{−6}$ m$^2$ ), 5.00 m length, and 5.10 m $\Omega$ resistance?

A researcher surveys people at a shopping mall about whether they favor enlarging the size of the mall parking lot. Explain why the following statement is misleading: “85% of the community is in favor of enlarging the parking lot.”

The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination.

$$\left\{ \begin{array} { r r } { 10 x + 10 y - 20 z = } & { 60 } \\ { 15 x + 20 y + 30 z = } & { - 25 } \\ { - 5 x + 30 y - 10 z = } & { 45 } \end{array} \right.$$

Represent the following problem in at least two ways. First, represent it as an expression containing only addition. Second, represent it as an expression containing addition and subtraction. While traveling in France, Juno was entertaining himself by riding in an elevator in a very tall building. He started at the ground floor (which in France is considered the 0th floor) and went up 26 floors. Then he rode down 7 floors. Next, he went up another 3 floors and then down again another 16 floors. What floor did Juno end up on?